Physical Pendulum Period

T = 2 π \frac{I}{m g d}

Period of a rigid body oscillating about a pivot point (physical/compound pendulum).

Variables

Period

Time for one oscillation

Moment of inertia

About pivot point

kg·m²

Mass

Total mass of pendulum

Gravitational acceleration

≈ 9.8 m/s²

m/s²

Distance to center of mass

From pivot to CM

Torque τ = -mgd·sin(θ) ≈ -mgdθ for small angles. Using τ = Iα: Iα = -mgdθ, giving ω² = mgd/I and T = 2π√(I/mgd).

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